Solve for $x$ and $y$ using elimination. ${-x+5y = 4}$ ${x-3y = 0}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $2y = 4$ $\dfrac{2y}{{2}} = \dfrac{4}{{2}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {-x+5y = 4}\thinspace$ to find $x$ ${-x + 5}{(2)}{= 4}$ $-x+10 = 4$ $-x+10{-10} = 4{-10}$ $-x = -6$ $\dfrac{-x}{{-1}} = \dfrac{-6}{{-1}}$ ${x = 6}$ You can also plug ${y = 2}$ into $\thinspace {x-3y = 0}\thinspace$ and get the same answer for $x$ : ${x - 3}{(2)}{= 0}$ ${x = 6}$